1.03 Module One Quiz 1. Two Martians, Splott and Fizzle, have solved the equation 2x + 4 = –3x + 14. Examine the work of Splott and Fizzle. Identify any errors in the Martians’ calculations and explain, using complete sentences, what corrections they should make. Q1 answer: The 4th row of Splott's calculation is unnecessary because he adds 4 instead of subtracting which leads to error on the next row.
Begin by writing the corresponding linear equations, and then use back-substitution to solve your variables. 10–1301–8001 159–1 x,y,z=( , , ) 10–1301–8001 159–1 = x-13z=15y-8z=9z=-1 = x-13(-1)=15y-8(-1)=9z=-1 = x=2y=1z=-1 x,y,z=(2 , 1 , -1) Determinants and Cramer’s Rule: 2. Find the determinant of the given matrix. 8–2–12 8–2–12 = 8*2 - (-1)(-2) = 16 - 2 = 14 3. Solve the given linear system using Cramer’s rule.
When you add the values 3, 5, 8, 12, and 20 and then divide by the number of values, the result is 9.6. Which term best describes this value: average, mean, median, mode, or standard deviation? Answer: 9.6 is the average of the numbers listed and is also the mean of this data. 4. Answer the next four questions using the following set of numbers.
| The legs have length '24' and 'X' are the legs. The hypotenuse is 26. See Picture | The hypotenuse is red in the diagram below: Step 2) Substitute values into the formula (remember 'c' is the hypotenuse) | A2 + B2 = C2 x2 + 242 = 262 | Step 3) Solve for the unknown | | Problem 1) Find the length of X | | Step 1 | Remember our steps for how to use this theorem. This problems is like example 1 because we are solving for the hypotenuse . Step 1) Identify the legs and the hypotenuse of the right triangle.
2x+3y=1200 Subtract 2x from both sides 3y= (1200-2x)/3 Slope= -2/3 Y intercept=1200/3=400 Y intercept=400 (0,400) 2. Describe how you would graph this line using the slope-intercept method. Be sure to write in complete sentences. First put a dot on (0,400) then use the slope to do the rest (two to the right and three down) 3. Write the equation in function notation.
Exponents, Scientific Notation, and Radicals Order of operations: Solve using the order of operations. Be sure to show each step to receive full credit. (–16 ÷ 2) × 4 – 3 + 82 (-8) x 4 (-32) -3+82 -29+ 82 - 372 Exponents: Define the product rule and the quotient rule in your own words. The product rule is a formal rule for differentiating problems where one function is multiplied by another. The quotient rule is a method of finding the derivative of a function that is the quotient of two other functions for which derivatives exist Using the product and quotient rule, solve the following: Product rule exercise: x^11* x^5= x^(11+5)=x^16 x^(–6 )* x^12 〖=x〗^(-6+12)=x^18 Quotient rule exercise: x^(30 )/x^10 = x^(30-10)=x^20 x^(30 )/x^(–10) =x^(30--10)=20 Scientific Notation: Refer to your textbook or any Internet source to answer the following question.
Problems Answer Grade Problem-1 a x+y=56 /3 b x+y=56 x+3x=56 56/4= 14 x=14 56-14=42 y=42 check 14+42=56 or 14+(14*3)=56 /3 c before we use elimination, we simplify the second equation by dividing by 25,000: new equation for b): 7x + 8y = 288 in order to eliminate a variable, multiply the first equation by -7: new equation for a): -7x + -7y = -266 Elimination: add the two equations and the x's cancel out: y = 22 x = 38-22 = 16 /3 d For the first equation, the intercepts are (56, 0) and (0,56). The intercept for the second equation is (0, 0). The lines would intersect at (14, 42) /3 Problem-2 a x+y=38 /3 b $175,000x+$200,000y=$7,200,000 /3 c Before we use elimination, we simplify the second equation
As a result from his knowledge, he solved the problem of finding the shortest and longest distances between one point and a conic. Many other Greek mathematicians studied conics, including Euclid and Pappus, but unfortunately, conic sections were basically ignored until the sixteenth century. Johannes Kepler discovered that the orbit of Mars made an ellipse with the sun as one of its foci. He soon found out this was the same with all planets and called it Kepler's First Law of Planetary Motion. Kepler also came up with the terms focus and directrix.
System of Non-Linear Equations Start this lesson by answering the warm-up questions below. This is to assess the ideas or concepts related to Non-linear and Linear equations. Activity 1.5.a Linear Against Non-Linear Equations Answer the following questions below: 1. Determine if the equation is linear or not a. 2x + 3y – 4 = 0 b. xy + 2 = 0 c. x = y d. y = 0 e. x = 2y + 3 2.
It sounds impossible to do, but it is actually not that difficult. The ONLY thing you ever do when solving a Rubik’s cube blindfolded is move a certain piece to a certain spot, do a certain algorithm, and then move that piece back to its original spot. The only problem is, you do that about thirty times (sometimes even more) each time you solve the cube blindfolded, and you need to memorize all of thirty of them before you close your eyes. Before we get started, I am going to explain the difference between orientation and permutation. Here’s a quick definition of each term.